Chapter 6 Practice Test
Assume the questions are non-calculator unless they involve decimals.



1.
Use integration to find a general solution of the differential equation.

A.
B.
C.
D.
E.


2.
Select from the choices below the slope field for the differential equation. Expect this to be non-calculator and not multiple choice.

A.

B.

C.

D.

E.
None of the above


3.
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 10 steps of size 0.05. Expect this to be non-multiple-choice, but a calculator question.

, y(0) = 4 .
A.
n
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
xn
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
yn
4.000
3.800
3.605
3.415
3.229
3.048
2.870
2.697
2.527
2.360
2.197
 
B.
n
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
xn
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
yn
4.000
4.300
4.105
3.915
3.729
3.548
3.370
3.197
3.027
2.860
2.697
 
C.
n
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
xn
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
yn
4.000
3.300
3.105
2.915
2.729
2.548
2.370
2.197
2.027
1.860
1.697
 
D.
n
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
xn
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
yn
4.000
3.550
3.355
3.165
2.979
2.798
2.620
2.447
2.277
2.110
1.947
 
E.
n
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
xn
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
yn
4.000
4.150
3.955
3.765
3.579
3.398
3.220
3.047
2.877
2.710
2.547
 


4.
Solve the differential equation.

A.
B.
C.
D.
E.
both A and D


5.
Write and solve the differential equation that models the following verbal statement:

The rate of change of V with respect to s is proportional to .
A.
,
B.
,
C.
,
D.
,
E.
,


6.
The isotope has a half-life of 1,599 years. After 15,000 years, a sample of the isotope is reduced 0.2 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,500 years? Round your answers to four decimal places.
A.
80.0023, 41.7552
B.
66.6686, 34.7960
C.
106.6697, 55.6736
D.
173.3383, 90.4695
E.
133.3371, 69.5920


7.
Find the general solution of the differential equation.

A.
B.
C.
D.
E.


8.
Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically.



A.
B.
C.
D.
E.
both A and C


9.
Find the orthogonal trajectories of the following family.

A.
B.
C.
D.
E.


10.
Find the equation that satisfies the following differential equation and initial condition.

, y(0) = 19
A.
B.
C.
D.
E.
None of the above.


11.
Solve the differential equation.

A.
B.
C.
D.
E.


12.
Find the particular solution of the differential equation that satisfies the boundary condition.

,
A.
B.
C.
D.
E.


13.
A 500 gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time t = 0, distilled water is admitted to the tank at a rate of 15 gallons per minute, and the well-stirred solution is withdrawn at the same rate.

(i) Find the amount of concentrate Q in the solution as a function of t.

(ii) Find the time at which the amount of concentrate in the tank reaches 15 pounds.

(iii) Find the quantity of the concentrate in the solution as .
A.
(i) ; (ii) 22.71 ; (iii) 1
B.
(i) ; (ii) 19.55 ; (iii) 0
C.
(i) ; (ii) 17.03 ; (iii) 0
D.
(i) ; (ii) 19.55 ; (iii) 1
E.
(i) ; (ii) 15.71 ; (iii) 0



STOP This is the end of the test. When you have completed all the questions and reviewed your answers, press the button below to grade the test.

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